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If A and G are respectively arithmetic a...

If A and G are respectively arithmetic and geometric mean between positive no. a and b ; then the quadratic equation having a;b as its roots is `x^2-2Ax+G^2=0`

A

`A=G`

B

`A=2 G`

C

`2A =G`

D

`A^(2)=G`

Text Solution

Verified by Experts

The correct Answer is:
a
Let `alpha and beta` be the roots of the equation
` x^(2) - 2ax +a^(2) = 0`
` :. Alpha + beta = 2a and alphabeta = a^(2) " " ` …(i)
Since, `A = (alpha + beta)/2 and G = sqrt(alpha beta)`
` rArr A = a and G^(2) = a^(2)` [ from Eq.(i)]
` rArr G^(2) = A^(2) rArr G = A `
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